Download presentation

Presentation is loading. Please wait.

1
**EEE 315 - Electrical Properties of Materials**

Lecture 2

2
Bravais Lattice The unit cell of a general 3D lattice is described by 6 numbers 3 distances (a, b, c) 3 angles (, , ) 25-Mar-17

3
Bravais Lattice There are 14 distinct 3D lattices which come under 7 Crystal Systems The BRAVAIS LATTICES (with shapes of unit cells as) : Cube (a = b = c, = = = 90) Square Prism (Tetragonal) (a = b c, = = = 90) Rectangular Prism (Orthorhombic) (a b c, = = = 90) 120 Rhombic Prism (Hexagonal) (a = b c, = = 90, = 120) Parallelepiped (Equilateral, Equiangular)(Trigonal) (a = b = c, = = 90) Parallelogram Prism (Monoclinic) (a b c, = = 90 ) Parallelepiped (general) (Triclinic) (a b c, ) 25-Mar-17

4
**Bravais Lattice The lattice centering are:**

Primitive (P): lattice points on the cell corners only. Body (I): one additional lattice point at the center of the cell. Face (F): one additional lattice point at the center of each of the faces of the cell. Base (A, B or C): one additional lattice point at the center of each of one pair of the cell faces. 25-Mar-17

5
Bravais Lattice 25-Mar-17

6
Miller Indices The planes passing through lattice points are called ‘lattice planes’. The orientation of planes or faces in a crystal can be described in terms of their intercepts on the three axes Miller introduced a system to designate a plane in a crystal. He introduced a set of three numbers to specify a plane in a crystal. This set of three numbers is known as ‘Miller Indices’ of the concerned plane. 25-Mar-17

7
**Miller Indices Miller indices is defined as the reciprocals of**

the intercepts made by the plane on the three axes. 25-Mar-17

8
**Miller Indices Procedure for finding Miller Indices**

Step 1: Determine the intercepts of the plane along the axes X,Y and Z in terms of the lattice constants a,b and c. Step 2: Determine the reciprocals of these numbers. 25-Mar-17

9
**Miller Indices Step 3: Find the least common denominator (lcd)**

and multiply each by this lcd. Step 4:The result is written in parenthesis. This is called the `Miller Indices’ of the plane in the form (h k l). 25-Mar-17

10
**Miller Indices ILLUSTRATION PLANES IN A CRYSTAL**

Plane ABC has intercepts of 2 units along X-axis, 3 units along Y-axis and 2 units along Z-axis. 25-Mar-17

11
**Miller Indices ILLUSTRATION DETERMINATION OF ‘MILLER INDICES’**

Step 1:The intercepts are 2,3 and 2 on the three axes. Step 2:The reciprocals are 1/2, 1/3 and 1/2. Step 3:The least common denominator is ‘6’. Multiplying each reciprocal by lcd, we get, 3,2 and 3. Step 4:Hence Miller indices for the plane ABC is (3 2 3) 25-Mar-17

12
**Miller Indices Example**

In this plane, the intercept along X axis is 1 unit. The plane is parallel to Y and Z axes. So, the intercepts along Y and Z axes are ‘’. Now the intercepts are 1, and . The reciprocals of the intercepts are = 1/1, 1/ and 1/. Therefore the Miller indices for the above plane is (1 0 0). 25-Mar-17

13
Miller Indices SOME IMPORTANT PLANES 25-Mar-17

14
**Miller Indices Problem # 1**

A certain crystal has lattice parameters of 4.24, 10 and 3.66 Å on X, Y, Z axes respectively. Determine the Miller indices of a plane having intercepts of 2.12, 10 and 1.83 Å on the X, Y and Z axes. Lattice parameters are = 4.24, 10 and 3.66 Å The intercepts of the given plane = 2.12, 10 and 1.83 Å i.e. The intercepts are, 0.5, 1 and 0.5. Step 1: The Intercepts are 1/2, 1 and 1/2. Step 2: The reciprocals are 2, 1 and 2. Step 3: The least common denominator is 2. Step 4: Multiplying the lcd by each reciprocal we get, 4, 2 and 4. Step 5: By writing them in parenthesis we get (4 2 4) Therefore the Miller indices of the given plane is (4 2 4) or (2 1 2). 25-Mar-17

15
**Miller Indices Problem # 2**

Calculate the miller indices for the plane with intercepts 2a, - 3b and 4c the along the crystallographic axes. The intercepts are 2, - 3 and 4 Step 1: The intercepts are 2, -3 and 4 along the 3 axes Step 2: The reciprocals are 1/2, -1/3, 1/4 Step 3: The least common denominator is 12. Multiplying each reciprocal by lcd, we get and 3 Step 4: Hence the Miller indices for the plane is 25-Mar-17

16
**Classical Theory of Electrical and Thermal Conduction**

25-Mar-17

17
**Electrical & Thermal Conduction**

Electrical conduction: Motion of charges (conduction electrons) in a material under the influence of an applied electric field Thermal conduction: Conduction of thermal energy from higher to lower temperature regions in a material Thermal conduction involves carrying of energy by conduction electrons. Good electrical conductors are also good thermal conductors! 25-Mar-17

18
Next Week! QUIZ! 25-Mar-17

Similar presentations

OK

EEE539 Solid State Electronics 1. Crystal Structure Issues that are addressed in this chapter include: Periodic array of atoms Fundamental types of.

EEE539 Solid State Electronics 1. Crystal Structure Issues that are addressed in this chapter include: Periodic array of atoms Fundamental types of.

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on world environment day activities Ppt on channel estimation Ppt on water conservation techniques Ppt on national education policy 1986 monte Ppt on digital energy meter Ppt on bombay stock exchange Ppt on working of nuclear power plant in india Ppt on etiquettes Ppt on renewable energy sources in india Download ppt on acid rain